Answer:
2. To evaluate the limit, we need to factor the numerator and the denominator of the fraction first:
√(2w+5)-3 / (2w-4) = [√(2w+5)-3] / [2(w-2)]
Now, we can see that the denominator becomes zero when w = 2. So, we need to check the limit separately for the left-hand and right-hand limits.
For the left-hand limit, as w approaches 2 from the left, the numerator approaches -3, and the denominator approaches a negative number very close to zero. So, the limit goes to negative infinity.
For the right-hand limit, as w approaches 2 from the right, the numerator approaches -3, and the denominator approaches a positive number very close to zero. So, the limit goes to positive infinity.
Since the left-hand limit and the right-hand limit are not equal, the limit does not exist.
Therefore, the answer is (E) The limit does not exist.
3. The derivative of f(x) = 5x + 2 is given by the formula:
f'(x) = d/dx (5x + 2) = 5
Therefore, the answer is (E) f(x)=- 35(5x + 2).